A rotary feed-through of this type for supplying a fluid to a rotating machine part is known from DE 102 25 272 A1. This rotary feed-through features a hollow shaft that is rotatably supported within a housing and has a first sliding surface, a sealing bushing that is arranged in the housing in a rotationally fixed fashion coaxial to the hollow shaft and has a second sliding surface for contacting the sliding surface of the hollow shaft, and a collecting chamber that is arranged within the housing and in which the leakage fluid escaping between the sliding surfaces of the rotating hollow shaft and the rotationally fixed sealing bushing can be collected. This collecting chamber is connected to a leakage opening, through which the leakage fluid collected in the collecting chamber can be discharged. Since only small quantities of the fluid being conveyed through the rotary feed-through usually escape at the interface between the two sliding surfaces, it normally suffices to occasionally drain or to permanently discharge via a corresponding line the leakage fluid collected in the collecting chamber. However, larger quantities of leakage fluid can escape in certain situations during operation. This is associated with the risk of the leakage fluid backing up within the collecting chamber such that the rotary feed-through may become damaged.